MMES: Mixture Model based Evolution Strategy for Large-Scale Optimization

• URL: http://arxiv.org/abs/2203.12675v1
• Date: Tue, 15 Mar 2022 14:33:37 GMT
• Title: MMES: Mixture Model based Evolution Strategy for Large-Scale Optimization
• Authors: Xiaoyu He and Zibin Zheng and Yuren Zhou
• Abstract summary: This work provides an efficient sampling method for the covariance matrix adaptation evolution strategy (CMA-ES) in large-scale settings. We analyze the probability distribution of this mixture model and show that it approximates the Gaussian distribution of CMA-ES with a controllable accuracy. We use this sampling method, coupled with a novel method for mutation strength adaptation, to formulate the mixture model based evolution strategy (MMES)
• Score: 36.37871629761407
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This work provides an efficient sampling method for the covariance matrix adaptation evolution strategy (CMA-ES) in large-scale settings. In contract to the Gaussian sampling in CMA-ES, the proposed method generates mutation vectors from a mixture model, which facilitates exploiting the rich variable correlations of the problem landscape within a limited time budget. We analyze the probability distribution of this mixture model and show that it approximates the Gaussian distribution of CMA-ES with a controllable accuracy. We use this sampling method, coupled with a novel method for mutation strength adaptation, to formulate the mixture model based evolution strategy (MMES) -- a CMA-ES variant for large-scale optimization. The numerical simulations show that, while significantly reducing the time complexity of CMA-ES, MMES preserves the rotational invariance, is scalable to high dimensional problems, and is competitive against the state-of-the-arts in performing global optimization.

Related papers

• Variational Learning of Gaussian Process Latent Variable Models through Stochastic Gradient Annealed Importance Sampling [22.256068524699472]
  In this work, we propose an Annealed Importance Sampling (AIS) approach to address these issues. We combine the strengths of Sequential Monte Carlo samplers and VI to explore a wider range of posterior distributions and gradually approach the target distribution. Experimental results on both toy and image datasets demonstrate that our method outperforms state-of-the-art methods in terms of tighter variational bounds, higher log-likelihoods, and more robust convergence.
  arXiv  Detail & Related papers  (2024-08-13T08:09:05Z)
• Adaptive Fuzzy C-Means with Graph Embedding [84.47075244116782]
  Fuzzy clustering algorithms can be roughly categorized into two main groups: Fuzzy C-Means (FCM) based methods and mixture model based methods. We propose a novel FCM based clustering model that is capable of automatically learning an appropriate membership degree hyper- parameter value.
  arXiv  Detail & Related papers  (2024-05-22T08:15:50Z)
• CatCMA : Stochastic Optimization for Mixed-Category Problems [9.13074910982872]
  Black-box optimization problems often require simultaneously optimizing different types of variables, such as continuous, integer, and categorical variables. Several Bayesian optimization methods can deal with mixed-category black-box optimization (MC-BBO), but they suffer from a lack of scalability to high-dimensional problems and internal computational cost. This paper proposes CatCMA, a new optimization method for MC-BBO problems.
  arXiv  Detail & Related papers  (2024-05-16T10:11:18Z)
• Gaussian Mixture Solvers for Diffusion Models [84.83349474361204]
  We introduce a novel class of SDE-based solvers called GMS for diffusion models. Our solver outperforms numerous SDE-based solvers in terms of sample quality in image generation and stroke-based synthesis.
  arXiv  Detail & Related papers  (2023-11-02T02:05:38Z)
• Multi-Response Heteroscedastic Gaussian Process Models and Their Inference [1.52292571922932]
  We propose a novel framework for the modeling of heteroscedastic covariance functions. We employ variational inference to approximate the posterior and facilitate posterior predictive modeling. We show that our proposed framework offers a robust and versatile tool for a wide array of applications.
  arXiv  Detail & Related papers  (2023-08-29T15:06:47Z)
• Optimization of Annealed Importance Sampling Hyperparameters [77.34726150561087]
  Annealed Importance Sampling (AIS) is a popular algorithm used to estimates the intractable marginal likelihood of deep generative models. We present a parameteric AIS process with flexible intermediary distributions and optimize the bridging distributions to use fewer number of steps for sampling. We assess the performance of our optimized AIS for marginal likelihood estimation of deep generative models and compare it to other estimators.
  arXiv  Detail & Related papers  (2022-09-27T07:58:25Z)
• CMA-ES with Margin: Lower-Bounding Marginal Probability for Mixed-Integer Black-Box Optimization [5.237999056930947]
  This study targets the mixed-integer black-box optimization (MI-BBO) problem where continuous and integer variables should be optimized simultaneously. We propose a simple modification of the CMA-ES based on lower-bounding the marginal probabilities associated with the generation of integer variables in the MGD.
  arXiv  Detail & Related papers  (2022-05-26T16:47:56Z)
• Permutation Invariant Policy Optimization for Mean-Field Multi-Agent Reinforcement Learning: A Principled Approach [128.62787284435007]
  We propose the mean-field proximal policy optimization (MF-PPO) algorithm, at the core of which is a permutation-invariant actor-critic neural architecture. We prove that MF-PPO attains the globally optimal policy at a sublinear rate of convergence. In particular, we show that the inductive bias introduced by the permutation-invariant neural architecture enables MF-PPO to outperform existing competitors.
  arXiv  Detail & Related papers  (2021-05-18T04:35:41Z)
• Sampling in Combinatorial Spaces with SurVAE Flow Augmented MCMC [83.48593305367523]
  Hybrid Monte Carlo is a powerful Markov Chain Monte Carlo method for sampling from complex continuous distributions. We introduce a new approach based on augmenting Monte Carlo methods with SurVAE Flows to sample from discrete distributions. We demonstrate the efficacy of our algorithm on a range of examples from statistics, computational physics and machine learning, and observe improvements compared to alternative algorithms.
  arXiv  Detail & Related papers  (2021-02-04T02:21:08Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.